This invention relates to electrical measuring devices, particularly devices such as digital multi-meters, adapted for determining the root-mean-square value of an electrical signal.
The root-mean-square ("RMS") value of an electrical signal is the effective value of the signal, or the DC equivalent of the signal that would dissipate the same power in a resistance as would the electrical signal. The average power dissipation in a resistor is proportional to the average of the squares of the amplitude of the signal at successive times (the "mean-square"). The effective or RMS value of the signal, then, is proportional to the square root of the mean-square. The present invention focuses on the mean-square portion of an RMS measurement which, in conjunction with taking the square root of the mean-square measurement, provides for the desired RMS value.
According to and in light of the mathematical definition of the RMS value of a signal, determining the RMS value has heretofore typically been accomplished by implementing the aforementioned mathematical operations, either in software or in hardware. That is, an electrical signal is sampled, the samples are individually squared, the squared samples are summed, the summed, squared samples are averaged and the square root is taken of the result.
In typical analog implementations of an RMS measuring circuit, analog multipliers, integrators and gain stages are employed to square the analog signal and average the results. Specialized devices whose gain characteristics approximate the square root function are then used to take the square root. These implementations are typically expensive and prone to error, as the physical implementations of the mathematical operations are difficult to realize.
Accordingly, it has become preferred to employ a digital implementation of an RMS measuring circuit. A typical digital implementation employs an analog-to-digital converter ("ADC") which produces a series of samples of the electrical signal ("an acquisition"), the series corresponding to a predetermined length of the electrical signal in time, the samples being provided to a processor for mathematically operating on the samples, again by squaring the samples, summing the squares of the samples, and taking the square root of the result. The process is repeated for a subsequent acquisition of the signal.
A source of error in the measurement of RMS results from measuring the mean-square by sampling the signal over a time period that, in general, is not equal to an integral number of quarter wave-lengths of the sinsusoidal ("Fourier") components of the signal. For a Fourier component, the average of the square of any quarter wave-length of the component is equal to the average of the square of the entire component. This will be some DC value "A". However, an arbitrary measured DC value for the component will be larger than "A" by the amount of signal energy contained in any fraction of a quarter wave-length of the original signal that is represented in the acquisition. This phase mis-match between the period of the Fourier components of an unknown signal and the period of the acquisition cannot, especially for signals having a large number of Fourier components, generally be accounted in the selection of the acquisition period, so that the error will generally fall somewhere between zero and the energy contained in a quarter wave-length of the signal. The phase mis-match error can be reduced, in general, only by increasing the acquisition interval and thereby dividing the error by an ever increasing number of samples in the process of averaging. The larger number of acquisitions causes a proportionate decrease in the output rate of the averaging process. Moreover, the processing time and hardware requirements, particularly memory requirements, are also increased.
The phase mis-match error will also, in general, vary from one acquisition to the next. Moreover, since the acquisitions are taken in discrete blocks or "chunks," the difference between the measured mean-square value for one acquisition and the measured mean-square value for another acquisition of a time varying signal may be significant. Therefore, the lack of overlap of the acquisitions assures that there will be, in general, "chunking" error manifest as "digit bobble." But providing for overlap in the acquisitions according to the prior art determination of the mean square to reduce digit bobble also increases the processing time and hardware requirements, particularly memory requirements.
Stated more broadly, the prior art method of measuring mean-square has comprised methods and apparatus for averaging a number of data points, wherein averaging is performed according to the text-book definition of the mean, i.e., adding the data points and dividing by the total number of data points. The only way to decrease the error in such averaging is to take more samples, inherently decreasing the rate of producing results. It would be desirable to employ a method and apparatus that is capable of decreasing error in a mean-square measurement that does not require the taking of more samples and, therefore, does not require a large number of devices to realize in hardware.
Accordingly, there is a need for a method and apparatus for measuring the mean-square value of an electrical signal that provides for improvement in minimizing error and reducing hardware cost, particularly the cost of large numbers of devices in an integrated circuit.